ABSTRACT:Rewritting the Navier-Stokes equations in terms of vorticity and velocity particle discretization of the vorticity field yields a classical N-body problem. The brute-force approach, in which all N*(N-1) mutual interactions between simulation particles are computed directly, inevitably becomes impractical. The mesh-free Barnes-Hut tree code approach reduces the number of direct particle-particle interactions through the systematic use of multipole expansions. In this talk we present our highly parallelized tree code PEPC and its capabilities, making it possible to perform simulations with many millions of particles. Originally designed for common Coulomb potentials the vortex particle methods require a generalization of the interaction kernels and their error terms. Furthermore, convergence in general vortex methods requires a strong condition on interparticle distances, which can now be addressed by parallel sorting without using an underyling grid structure. Being already a fundamental part of tree codes the overhead of this additional sorting process -- the 'remeshing' step -- is negligible.

BIO:Robert Speck received his Diploma in Applied Mathematics with focus on complex analysis at the University of Trier in 2007. Starting from 2007 he is currently working at Juelich Supercomputing Centre (Simulation Laboratory Plasma Physics) on parallel tree codes for vortex particle methods in collaboration with the Universities of Wuppertal and Lugano.